A US company has a current total market value of $$12$ billion, consisting of $$10$

billion of equity and $$2$ billion of debt capital. The debt capital will mature in four

years' time. The current weighted average cost of capital is $6\mathrm{.}5\%.$

The company is considering a new investment costing $$3$ billion, which it would

finance entirely by $$3$ billion of new ten$-$year bonds.

The yield curve for US government bonds $($Treasuries$)$ shows that the risk$-$free cost

of four$-$year debt is $4\%$ and the risk$-$free cost of ten$-$year debt is $4\mathrm{.}25\%.$ The credit

rating on the company's current debt capital is AA$,$ but if the new bond issue takes

place there is a $75\%$ probability that all the company's debt will be re$-$rated to AA$-$

and a $25\%$ probability that all the company's debt will be re$-$rated to At$.($This

applies to both the existing debt and the new bonds.$)$

The spreads for yields on corporate bonds above the US Treasuries yield curve are

as follows:

The rate of taxation on company profits is $30\%$

Required

Calculate the weighted average cost of capital in the company if the project goes

ahead and is financed entirely by ten$-$year bonds. Assume that there will be no

change in the company's business risk.